# Correlation of Fixed Effects in lmer

I'm a psycholinguistics student with few knowledge in statistics and I have some doubts about a Correlation of Fixed Effects in lmer function (lme4 package).

My response variable is RT (Reaction Time in a self-paced reading experiment) and my independent variables are Ant (PP, NP) and Verbo (SG, PL).

I have modeled the data with intercepts for Sujeitos (the people who are doing the task) and Item (the sentences i've used), asking for principal effects and interactions between the variables. Here is the model lmer(RT~Ant*Verbo+(1|Sujeitos)+(1|Item)) and that's the coefficients for fixed effects: So, I have made a table of the coefficients for the interactions.

My problem is: that -0.705 and -0.716 correlation effects are a problem for my interaction terms? I'm saying this because the coefficients for the condition NP:SG came from the coefficients of SG only: and the coefficients for PP:PL came from the PP only: So, to me, there is no problem here, because I'm not contrasting PP:SG x PP (correlation = -0.705) and I'm not contrasting PP:SG x SG ((correlation = -0.716)). But I do that when getting the coefficients for PP:SG: In the last case, there is a contrast between PP:SG x PP and SG. So, the correlation could be a problem. Is this correct? And, if so, how can I deal with this? I've read some thinks in Jaeger's blog and in this book: Howell, 2010. Statistical Methods for Psychology, but it doesn't help much.

Thank you.

No, it is not a problem. The correlation arises from the fact that your two categorical predictors are entered as dummy codes, and are therefore not orthogonal to the interaction term, even in the case of balanced data. So we fully expect both the predictors themselves (i.e., the vectors of predictor values) and the parameter estimates to be correlated. It is exactly the same issue in fixed-effects-only regression using, for example, lm().
If you want, you can recode your categorical predictors using sum-to-zero contrasts (e.g., contr.helmert(2)), and the correlations between the interaction and simple effects should be lessened. But it shouldn't make any difference as far as the test of the interaction term is concerned.